Simple models for two and three dimensional particle size segregation

The segregation of binary particle mixtures has been investigated using simple two and three dimensional models in which particles are deposited one at a time with the same lateral position on a growing heap of particles. After deposition the particles follow a path of steepest descent on the heap until they reach a local minimum, contact the substrate or reach the walls of a containing vessel. For large values of the diameter ratio, r (r = dL/ds where ds is the small particle diameter and dL is the large particle diameter) the width of the large particle depletion region near the center of the heap is directly proportional to the area ratio φ (φ = d2sNs/d2LNL where Ns and NL are the number of small and large particles respectively) for two dimensional heaps. A qualitatively similar structure has been found for the deposition of a binary mixture of spheres into a vertical cylinder but we have not been able to carry out large enough simulations to measure the dependence of the core depletion width on r and φ. Other measures of the degree of segregation do show that the degree of segregation increases with increasing r and φ for three dimensional cases. For example, the three dimensional simulations indicate that (R̄2L)12 - (R̄2s)12 ∼ r2φ12 where R is the distance from the cylinder axis.